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    Quantum Contextuality with Stabilizer States


    Howard, Mark and Brennan, Eoin and Vala, Jiri (2013) Quantum Contextuality with Stabilizer States. Entropy, 15. pp. 2340-2362. ISSN 1099-4300

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    Abstract

    The Pauli groups are ubiquitous in quantum information theory because of their usefulness in describing quantum states and operations and their readily understood symmetry properties. In addition, the most well-understood quantum error correcting codes—stabilizer codes—are built using Pauli operators. The eigenstates of these operators—stabilizer states—display a structure (e.g., mutual orthogonality relationships) that has made them useful in examples of multi-qubit non-locality and contextuality. Here, we apply the graph-theoretical contextuality formalism of Cabello, Severini and Winter to sets of stabilizer states, with particular attention to the effect of generalizing two-level qubit systems to odd prime d-level qudit systems. While state-independent contextuality using two-qubit states does not generalize to qudits, we show explicitly how state-dependent contextuality associated with a Bell inequality does generalize. Along the way we note various structural properties of stabilizer states, with respect to their orthogonality relationships, which may be of independent interest.

    Item Type: Article
    Additional Information: The definitive version of this article is available at Howard, M.; Brennan, E.; Vala, J. Quantum Contextuality with Stabilizer States. Entropy 2013, 15, 2340-2362. M.H. was financially supported by the Irish Research Council (IRC) as part of the Empower Fellowship program. J.V. acknowledges support from Science Foundation Ireland under the Principal Investigator Award No. 10/IN.1/I3013. We thank Joseph Emerson for helpful comments on a previous version of this manuscript. Published under a Creative Commons Attribution License
    Keywords: contextuality; stabilizer; non-locality;
    Academic Unit: Faculty of Science and Engineering > Mathematical Physics
    Item ID: 5565
    Identification Number: https://doi.org/10.3390/e15062340
    Depositing User: Dr. Jiri Vala
    Date Deposited: 19 Nov 2014 16:00
    Journal or Publication Title: Entropy
    Publisher: MDPI
    Refereed: Yes
    Funders: Irish Research Council, Science Foundation Ireland
    URI:

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